Perturbations and Vertex Removal in Delaunay and Regular 3D Triangulations

Though Delaunay and regular triangulations are very well known geometric data structures, the problem of the robust removal of a vertex in a three-dimensional triangulation is actually a problem in practice. We propose a simple method that allows to remove any vertex even when the points are in very degenerate configurations. The solution is available in CGAL (www.cgal.org).